Radioactive materials are used in a number of everyday applications and in medicine. A hospital uses a radioactive isotope as a tracer to investigate the fu...
Question 1 Report
Radioactive materials are used in a number of everyday applications and in medicine. A hospital uses a radioactive isotope as a tracer to investigate the functioning of a patient's thyroid gland. A small quantity of iodine-131 is administered to the patient by injection. The isotope accumulates in the thyroid gland and its radiation can be detected externally. The doctor monitors the uptake of iodine-131 in the thyroid gland over a period of several days using a gamma camera positioned near the patient's neck. Iodine-131 has a half-life of 8.0 days and emits beta particles and gamma rays. The effective half-life inside the body is shorter than 8.0 days because the body also excretes the iodine naturally. The activity of the sample at the time of injection is 4.0 MBq.
(a) State what is meant by the term half-life of a radioactive isotope. [2]
(b) Explain why a gamma-emitting isotope is chosen for this application rather than one that emits only alpha particles. [2]
(c) The effective half-life inside the body is 5.0 days. Calculate the activity of the iodine-131 in the thyroid gland after 15 days. [3]
Answer Details
(a) Definition of half-life [2]
The half-life of a radioactive isotope is the time taken for the activity of the sample to decrease to half its original value. [1] Equivalently, it is the time taken for half the undecayed nuclei in a sample to decay. [1]
Both definitions are equivalent: as half the nuclei decay, the number of decays per second (activity) also halves.
(b) Why a gamma-emitting isotope is chosen [2]
Gamma rays are highly penetrating and can pass through body tissue to be detected by the gamma camera positioned outside the patient's neck. [1] Alpha particles would be absorbed within millimetres of tissue and would never reach the external detector. Additionally, alpha particles are highly ionising and would cause excessive damage to the surrounding cells. [1]
(c) Activity after 15 days [3]
The effective half-life inside the body is 5.0 days (shorter than the physical half-life of 8.0 days because the body also excretes the iodine).
Number of half-lives in 15 days:
\(n = \frac{15}{5.0} = 3\) [1]
After 3 half-lives, the activity is:
\(A = 4.0 \times \left(\frac{1}{2}\right)^3 = \frac{4.0}{8}\) [1]
\(A = \mathbf{0.50 \text{ MBq}}\) [1]
Step by step: 4.0 \(\rightarrow\) 2.0 \(\rightarrow\) 1.0 \(\rightarrow\) 0.50 MBq.
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